We study the penetration field $H_{rm P}$ for vortex nanocrystals nucleated in micron-sized samples with edges aligned along the nodal and anti-nodal directions of the d-wave superconducting parameter of Bi$_2$Sr$_2$CaCu$_2$O$_{8 - delta}$. Here we p
resent evidence that the $H_{rm P}$ for nanocrystals nucleated in samples with edges parallel to the nodal direction is larger than for the antinodal case, $sim 72$,% at low temperatures. This finding supports the theoretical proposal that surface Andreev bound states appearing in a sample with edges parallel to the nodal direction would produce an anomalous Meissner current that increases the Bean-Livingston barrier for vortex penetration.This has been detected thanks to the nucleation of vortex nanocrystals with a significant surface-to-volume ratio.
We study the effect of quenched disorder in the thermodynamic magnitudes entailed in the first-order vortex phase transition of the extremely layered Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8 + delta}$ compound. We track the temperature-evolution of the enthal
py and the entropy-jump at the vortex solidification transition by means of AC local magnetic measurements. Quenched disorder is introduced to the pristine samples by means of heavy-ion irradiation with Pb and Xe producing a random columnar-track pins distribution with different densities (matching field $B_{Phi}$). In contrast with previous magneto-optical reports, we find that the first-order phase transition persists for samples with $B_{Phi}$ up to 100,Gauss. For very low densities of quenched disorder (pristine samples), the evolution of the thermodynamic properties can be satisfactorily explained considering a negligible effect of pinning and only electromagnetic coupling between pancake vortices lying in adjacent CuO planes. This description is not satisfactory on increasing magnitude of quenched disorder.
We study geometrical confinement effects in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8 +delta}$ mesoscopic vortex-matter with edge-to-surface ratio of $7-12$%. Samples have in-plane square and circular edges, 30,$mu$m widths, and $sim 2,mu$m thickness. Direct v
ortex imaging reveals the compact planes of the structure align with the sample edge by introducing topological defects. The defects density is larger for circular than for square edges. Molecular dynamics simulations suggest this density is not an out-of-equilibrium property but rather determined by the geometrical confinement.
The persistence of the first-order transition line in the phase diagram of mesoscopic Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8}$ vortex matter is detected down to a system size of less than hundred vortices. Precise and highly-sensitive to bulk currents AC ma
gnetization techniques proved to be mandatory in order to obtain this information. The location of the vortex matter first-order transition lines are not altered by decreasing the sample size down to 20 $mu$m. Nevertheless, the onset of irreversible magnetization is affected by increasing the sample surface-to-volume ratio producing a noticeable enlargement of the irreversible vortex region above the second-peak transition.
